An intelligent inversion method for warehouse entry flow based on multi-source error constraint fusion

Abstract

This invention provides an intelligent inversion method for inflow based on multi-source error constraint fusion, belonging to the field of hydrological forecasting technology. The method includes: constructing physical constraints based on long-sequence water level observation data, measured outflow sequences, and reservoir capacity-water level curves; constructing a composite optimization function including a reservoir capacity time-varying error compensation term, inflow continuity regularization constraints, and a water level observation data assimilation module; deriving the analytical inversion solution of inflow based on the Lagrange multiplier method; and automatically optimizing key parameters such as constraint weights and smoothing coefficients using intelligent optimization methods such as grid search and cooperative search algorithms to perform adaptive high-precision inversion under different hydrological scenarios. This invention, by dynamically adjusting the error weight coefficients, directly generates physically consistent inflow sequences without relying on the prior assumptions of traditional smoothing filters, significantly improving the performance of negative value rate control, water balance, and flood peak characteristic preservation.

Description

Technical Field

[0001] This invention relates to the field of hydrological forecasting technology, and in particular to an intelligent inversion method for inflow based on multi-source error constraint fusion. Background Technology

[0002] Reservoir inflow is a core foundational data source for hydrological forecasting, reservoir scheduling, and water resources management. Its inversion accuracy directly impacts the safety and economic efficiency of water conservancy projects. Currently, inflow inversion methods based on the water balance principle typically assume accurate water level observations, a stable and reliable reservoir capacity-water level curve, and no significant deviations in outflow measurements. However, in real-world engineering environments, these conditions are difficult to fully meet. Factors such as gate opening / closing status changes, fluctuations in upstream and downstream head differences leading to outflow monitoring noise, the inability to monitor latent outflows like dam seepage and ecological releases, time-varying shifts in the reservoir capacity-water level curve caused by long-term siltation, and random errors from instrument accuracy and wave disturbances affecting water level observations all contribute to the cumulative amplification of these multi-source errors. This results in the traditional inversion method outputting inflow sequences often exhibiting severe sawtooth oscillations, and even physically unreasonable negative values, severely impacting data reliability.

[0003] Currently, existing technologies have proposed some optimization schemes to improve flow fluctuations by adjusting the time period and water volume correction. However, they do not explicitly model multi-source errors and rely solely on single real-time error control. This cannot suppress the cumulative impact of systematic errors such as time-varying reservoir capacity and hidden outflow. The constraint system is too simplistic and lacks sufficient physical rationality. While simulating flow smoothing processes through machine learning models can reduce fluctuations, it relies on a large amount of sample data for training, which limits its generalization ability. Furthermore, it does not incorporate core hydrological physical constraints (such as water conservation and non-negativity), which can easily lead to the loss of flood peak characteristics or violation of physical laws, making it unsuitable for complex hydrological scenarios. Summary of the Invention

[0004] The purpose of this invention is to provide an intelligent inversion method for reservoir inflow based on multi-source error constraint fusion. This method addresses the challenges of multi-source error interference, insufficient parameter optimization, and poor stability of inversion results in reservoir inflow inversion. By constructing an optimization function that includes a reservoir capacity time-varying error compensation term, inflow continuity regularization constraints, and a water level observation data assimilation module, and deriving an analytical solution based on the Lagrange multiplier method, the method combines grid search and cooperative search algorithms to optimize key parameters such as constraint weights and smoothing coefficients, thereby achieving high-precision and refined inversion of reservoir inflow.

[0005] To achieve the above objectives, this invention proposes an intelligent inversion method for inbound traffic based on multi-source error constraint fusion, comprising the following steps: Step S1: Preprocess and normalize the water level and outflow monitoring data; Step S2: Construct a composite optimization function that includes a reservoir capacity time-varying error compensation term, inflow continuity regularization constraints, and a water level observation data assimilation module, including the following steps: Step S21: Obtain the original data of the reservoir's measured capacity-water level curve. Construct a nonlinear curve constraint through fitting to characterize the mapping relationship between the reservoir's water level and capacity. Based on the original inflow data, embed the constraint into the optimization function, enforce the constraint through a penalty term, and construct the inflow constraint. This constraint defines the physical boundary of the inverted flow. Combine the outflow monitoring error, implicit outflow error, and water level-capacity error into a single capacity error, and introduce it into the water balance formula to achieve adaptive error adjustment. Construct the water balance equation, which is: ; in, for The reservoir capacity value corresponding to the water level at a given time. for The reservoir capacity value corresponding to the water level at a given time. for Inbound volume at any given time for Outbound volume at any given time For a moment The reservoir capacity error value; Step S22: Incorporate the temporal variation characteristics of the flow sequence into the optimization framework to construct a smoothness constraint on inflow within continuous time periods, as shown in the formula: ; in, for Inbound volume at any given time The sequence length of the inbound flow. To obtain the minimum value; Step S23: Construct and solve the optimization function expression. The optimization function expression is: ; in, and They are Observed and estimated water levels at any given time; For a moment Reservoir capacity error value, For smoothing coefficients, , For constrained weights ; Step S3: Based on the Lagrange multiplier method, a unified expression of physical constraints such as nonnegativity, continuity, and water conservation is used to derive the analytical inversion solution for the inflow and outflow. This includes the following steps: Step S31: Based on the Lagrange optimization principle, transform the optimization function into a matrix equation containing state variables and error variables. The specific dimensions and structure are as follows: ; ; ; in, , , , The coefficient submatrix, whose specific elements are determined by the boundary conditions and the equations of the interior points, For the state variable vector, For the error variable vector, To observe the reservoir capacity corresponding to the water level, , , They are respectively the dimensions of , , Known variables , The coefficient matrix, for The 0 matrix, To solve for the coefficient matrix of the variables, To solve for the variable vector, It is a constant vector; Step S32: Optimize the constraint weights and smoothing coefficients using grid search or cooperative search algorithms. Specifically, use grid search to systematically traverse the smoothing coefficients, and use cooperative search to perform global optimization of the combination of constraint weights and smoothing coefficients and solve the matrix. Reconstruct the linear matrix equation constraints into a least-squares optimization objective, solve for the optimal solution by minimizing the squared residual between the predicted and observed values, and determine whether the result meets the physical constraints and evaluation index requirements. Step S33: For matrix equations that do not meet the physical constraints and evaluation index requirements, reconstruct them into augmented matrices containing explicit constraint operators, where explicit constraint operators include boundary constraints, smoothing constraints, trend constraints and water balance constraints, and the four types of constraint operators work together. Step S34: Perform trial calculations on the adjustment coefficients of the physical constraint terms in the augmented matrix or automatically optimize the hyperparameters based on the cooperative search algorithm, and solve the augmented matrix after adjusting the magnitude of the constraint terms; Step S4: Output the solution variable results that meet the physical constraints and evaluation index requirements.

[0006] Preferably, step S1 includes the following steps: Step S11: Align the raw monitoring data with the time dimension to ensure that the key data are strictly consistent at the time nodes. The key data includes, but is not limited to, water level and outflow. Step S12: For individual missing values, use linear interpolation to complete them; Step S13: Based on the reservoir water level-capacity relationship curve, convert the discrete water level time series into the corresponding reservoir capacity time series to generate the dynamic change data of reservoir capacity required for model operation. The normalization formula is as follows: ; in, For numerical sequences that require normalization calculations, For data sequences that need to be standardized, For sequence The midpoint value of the sequence after sorting from largest to smallest This is the standardized data.

[0007] Preferably, step S21 includes the following steps: Step S211: Construct nonlinear curve constraints to characterize the mapping relationship between reservoir water level and reservoir capacity, ensuring the physical correspondence between reservoir capacity estimation and water level observation. The formula is: ; in, This is the water level-capacity curve of the reservoir. for The water level at that moment; Step S212: Construct inbound quantity constraints to constrain the physically reasonable boundaries of the inverted flow, avoiding physically unreasonable negative flow values. The formula is: ; in, for The original inbound flow at any given moment for Time's up The time interval between moments; Step S213: Construct outbound quantity constraints to strictly control the outbound flow rate to be greater than or equal to 0. The formula is: ; in, for The original outbound flow at any given moment.

[0008] Preferably, in step S23, the flow smoothing term in the optimization function characterizes the natural runoff process that is not significantly regulated by human activities by constraining the slow variability of inflow over a short period of time. When human activities have a strong effect on runoff regulation in the study area, the applicability of the simplification assumption is reduced, and the optimization strategy is adjusted in combination with the actual hydrological situation.

[0009] Preferably, step S31 includes the following steps: Step S311: Substitute the nonlinear curve constraints, inflow constraints, outflow constraints, and water balance constraints into the optimization function, transforming the optimization function into a function expression containing known and unknown variables. The formula is as follows: ; in, for The reservoir capacity value corresponding to the water level at a given moment; Step S312: Based on the Lagrange optimization principle, take partial derivatives with respect to the unknown variables to obtain two partial differential equations. Set the partial differential equations to zero, rearrange them to form a system of equality constraint equations, and calculate... , Internal points Boundary points and expanding boundary points Equality constraints at that time; Step S313: Further rearrange the system of equality constraint equations into matrix form.

[0010] Preferably, in step S31: ; ; ; ; ; The state variable vector and error variable vector can be solved by matrix inversion, using the following formula: ; in, This is the matrix transpose.

[0011] Preferably, step S32 includes the following steps: Step S321: Use a grid search algorithm to smooth the low-dimensional parameter coefficients. Perform a systematic traversal, the traversal range is Initial screening identified smoothing coefficients that balance flow smoothness with observation fit. Candidate values; Step S322: Use a cooperative search algorithm to adjust the constraint weights. With smoothing coefficient Global optimization is performed using high-dimensional coefficient combinations, with the optimization range being... , The optimization objective is to minimize the value of the composite optimization function while simultaneously satisfying the inflow rate. Preliminary physical constraints; Step S323: Solve the matrix equation using the least squares method This yields the initial storage capacity state variables and storage capacity error variables; Step S324: Calculate the inflow rate based on the initial solution results, and determine whether it meets the preset physical constraints and evaluation indicators. If it meets the requirements, proceed to step S4; otherwise, proceed to step S33.

[0012] Preferably, in step S33, the standard form is transformed into an augmented matrix form containing explicit constraint operators. This involves the following steps to explicitly construct boundary constraints, smoothing constraints, trend constraints, and water balance constraints for solving the pool capacity, error, and other variables: Step S331: Reconstruct the linear matrix equation constraints into a least-squares optimization objective, and solve for the optimal solution by minimizing the squared residuals between the predicted and observed values. The formula is as follows: ; in, for The squared 2-norm of the residual vector of a matrix equation is mathematically expressed as the sum of the squares of the elements of the residual vector, i.e. ; Step S332: Explicitly construct boundary constraints, smoothing constraints, trend constraints, and water balance constraints for the solution variables, including: Boundary constraints: control the amplitude range of state variables and suppress excessive amplification of model residuals and observation errors. The formula is: ; in, This is the adjustment coefficient for variable storage capacity; the reference range is... , This is the adjustment coefficient for the variable error tolerance; the reference range is... ; Smoothing constraint: controls the smoothness of time-varying state variables, the formula is: ; ; ; in, This is the adjustment coefficient for the rate of change in storage capacity. Let the first difference of the state variable, storage capacity, represent the rate of change of storage capacity. This is the adjustment coefficient for the rate of change of storage capacity error. The first difference of the variable error represents the rate of change of the error; , The reference value range is Adjust the value according to the magnitude; Trend constraint: Constrains the smoothness of second-order changes in state variables, with the following formula: ; ; in, This is a trend adjustment coefficient, with a reference range of values. , The second difference of the state variable represents the trend of the state variable's change; Water balance constraint: By constraining the balance between reservoir capacity error, reservoir capacity change, and inflow / outflow, an augmented matrix is ​​added as a penalty term during the calculation to suppress solutions that violate water conservation. The formula is as follows: ; ; ; in, These are the weighting coefficients for water balance constraints. For length is The vector, To solve for the variable vector, The storage capacity value at the final moment of the input sequence. for Real-time inbound volume for Real-time outbound volume; Step S333: Combine the least squares terms of the fundamental matrix, the constraint terms for storage capacity, and the constraint terms for storage capacity error to obtain the overall objective function, the formula of which is: ; Step S334: Rewrite the overall objective function in matrix form to obtain the augmented matrix form, as shown in the formula: ; ; ; in, To solve for the augmented coefficient matrix of the variables, A constant vector in its augmented form; Step S335: Solve the overall objective function in augmented matrix form to obtain the unknown variables storage capacity and storage capacity error, as shown in the formula: ; in, is the matrix regularization coefficient.

[0013] Preferably, step S34 specifically involves: determining the adjustment coefficient of the model constraint term based on the magnitude difference of the input sequences, using either a trial-and-error algorithm or a cooperative search algorithm. , , , and Adjust the magnitude of the constraint terms and solve for the augmented matrix.

[0014] Therefore, this invention proposes an intelligent inversion method for inbound flow based on multi-source error constraint fusion, the beneficial effects of which are as follows: (1) This invention can effectively suppress the cumulative amplification effect of outflow noise, water level error and implicit outflow disturbance on the inversion process by explicit modeling of multi-source error and construction of multiple constraints.

[0015] (2) This invention uses Lagrange multipliers to uniformly express physical constraints such as non-negativity, continuity, and water conservation, so that the inversion results meet the basic laws of hydrology and avoid negative values ​​and unreasonable jumps.

[0016] (3) The present invention retains the real fluctuation process while smoothing noise, so that the size of the flood peak, arrival time and trend change remain reliable, providing more reliable input data for scheduling applications.

[0017] (4) The present invention enables the model to automatically adjust the constraint strength according to the water level observation accuracy, the degree of reservoir capacity curve deviation and the noise intensity through the parameter optimization mechanism, thereby improving the generalization ability.

[0018] (5) The present invention adopts the analytical matrix solution method, which avoids the numerical oscillation problem of traditional methods. It has the advantages of strong repeatability and high computational efficiency, and is suitable for long sequence and high frequency data processing. Attached Figure Description

[0019] Figure 1 This is a flowchart of an intelligent inversion method for inbound traffic based on multi-source error constraint fusion; Figure 2 A comparison chart showing the calculation results based on the grid search method and the comparison method; Figure 3 This is a graph showing the calculation results of an intelligent inversion method for inbound flow based on multi-source error constraint fusion and a cooperative search algorithm. Detailed Implementation

[0020] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0021] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0022] Example 1 like Figure 1 As shown, this invention provides an intelligent inversion method for inflow based on multi-source error constraint fusion. The method selects the daily runoff sequences of two reservoirs as the research object and includes the following steps: Step S1: Preprocess and normalize the water level and outflow monitoring data, including the following steps: Step S11: First, align the original monitoring data in terms of time dimension to ensure that key data such as water level and outflow are strictly consistent in time nodes, so as to avoid subsequent calculation deviations due to time misalignment. Step S12: For individual missing values, use linear interpolation to complete them, ensuring the continuity of the data sequence; Step S13: Based on the reservoir water level-capacity relationship curve, convert the discrete water level time series into the corresponding reservoir capacity time series to generate the dynamic change data of reservoir capacity required for model operation. The normalization formula is as follows: ; in, For numerical sequences that require normalization calculations, For data that needs to be standardized, For sequence The midpoint value of the sequence after sorting from largest to smallest This is the standardized data.

[0023] Step S2: Construct a composite optimization function that includes a reservoir capacity time-varying error compensation term, inflow continuity regularization constraints, and a water level observation data assimilation module, including the following steps: Step S21: Construct nonlinear curve constraints, inflow constraints, outflow constraints, and water balance constraints to characterize the mapping relationship between reservoir water level and reservoir capacity, constrain the physical reasonable boundary of the inverted flow, and ensure that the outflow value is strictly non-negative and meets the water balance requirements. This includes the following steps: Step S211: Construct nonlinear curve constraints to characterize the mapping relationship between reservoir water level and reservoir capacity, ensuring the physical correspondence between reservoir capacity estimation and water level observation. The formula is: ; in, This is the water level-capacity curve of the reservoir. for The water level at that moment; Step S212: Construct inbound quantity constraints to constrain the physically reasonable boundaries of the inverted flow, avoiding physically unreasonable negative flow values. The formula is: ; in, for The original inbound flow at any given moment for Time's up The time interval between moments; Step S213: Construct outbound quantity constraints, strictly controlling the outbound flow rate to be greater than or equal to 0, i.e., the outbound quantity must be non-negative. The formula is: ; in, for The original outbound flow at any given moment.

[0024] Step S214: Construct a water balance equation, combining outflow monitoring error, implicit outflow error, and water level / storage capacity error into a single storage capacity error. Introduce a water balance formula to achieve adaptive error adjustment, ensuring the results have good physical rationality and stability. The formula is: ; in, for The reservoir capacity value corresponding to the water level at a given time. for The reservoir capacity value corresponding to the water level at a given time. for Inbound volume at any given time for Outbound volume at any given time For a moment The reservoir capacity error value; Step S22: Construct a smoothness constraint for inflow within a continuous time period to suppress sawtooth fluctuations in the inflow sequence; specifically, to characterize the stable change characteristics of inflow within a continuous time period, the temporal variation characteristics of the flow sequence are incorporated into the optimization framework to accurately reflect the slow evolution characteristics of natural inflow under conditions of no significant human activity interference. The formula is: ; in, for Inbound volume at any given time The sequence length of the inbound flow. To obtain the minimum value; Step S23: Construct and solve the optimization function expression. The optimization function expression is: ; in, and They are Observed and estimated water levels at any given time; For a moment Reservoir capacity error value, For smoothing coefficients, Used to balance the weights of the smoothing term and the observation-fit term. To constrain the weights, Used to control the strength of the error penalty term.

[0025] In the objective function, the flow smoothing term characterizes the natural runoff process that is not significantly regulated by human activities by constraining the slow variability of inflow over a short period of time. When human activities (such as water conservancy project scheduling, irrigation water diversion, etc.) have a strong effect on runoff regulation in the study area, the applicability of this simplification assumption will be reduced, and the optimization strategy needs to be adjusted according to the actual hydrological situation.

[0026] Step S3: Based on the Lagrange multiplier method, a unified expression of physical constraints such as nonnegativity, continuity, and water conservation is used to derive the analytical inversion solution for the inflow and outflow. This includes the following steps: Step S31: Based on the Lagrange optimization principle, transform the optimization function into a matrix equation containing state variables and error variables, including the following steps: Step S311: Substitute the nonlinear curve constraints, inflow constraints, outflow constraints, and water balance constraints into the optimization function, transforming the optimization function into one containing known variables ( and ) and unknown variables ( and The function expression for ) is: ; in, for The reservoir capacity value corresponding to the water level at a given moment; Step S312: Based on the Lagrange optimization principle, take partial derivatives with respect to the unknown variables to obtain two partial differential equations, the formulas of which are: ; ; Setting the partial differential equation to zero, we can rearrange it to form a system of equality constraint equations, as follows: ; when hour: ; when hour: ; when Time (internal point): ; when hour( Boundary points): ; when hour( (Extended boundary points) ; Step S313: Rearrange the equality constraints into matrix form. The specific dimensions and structure are as follows: ; ; ; in, , , , The coefficient submatrix, whose specific elements are determined by the boundary conditions and the equations of the interior points, For the state variable vector, For the error variable vector, To observe the reservoir capacity corresponding to the water level, , , They are respectively the dimensions of , , Known variables , The coefficient matrix, for The 0 matrix, To solve for the coefficient matrix of the variables, the matrix dimension is... , To solve for the variable vector, the matrix dimension is... , It is a constant vector with matrix dimension . ; For ease of calculation, the coefficient matrices are all in sparse matrix form. The specific descriptions of each coefficient matrix are as follows: ; ; ; ; ; The state variable vector and error variable vector can be solved by matrix inversion, using the following formula: ; in, This is the matrix transpose.

[0027] Step S32: Optimize the constraint weights and smoothing coefficients using a grid search or cooperative search algorithm. Specifically, this involves: systematically traversing the smoothing coefficients using a grid search; globally optimizing the combination of constraint weights and smoothing coefficients using a cooperative search and solving the matrix; reconstructing the linear matrix equation constraints into a least-squares optimization objective; finding the optimal solution by minimizing the squared residual between the predicted and observed values; and determining whether the result meets the physical constraints and evaluation criteria. This includes the following steps: Step S321: Use a grid search algorithm to smooth the low-dimensional parameter coefficients. Perform a systematic traversal, the traversal range is Initial screening identified smoothing coefficients that balance flow smoothness with observation fit. Candidate values; Step S322: Use a cooperative search algorithm to adjust the constraint weights. With smoothing coefficient Global optimization is performed using high-dimensional coefficient combinations, with the optimization range being... , The optimization objective is to minimize the value of the composite optimization function while simultaneously satisfying the inflow rate. Preliminary physical constraints; Step S323: Solve the matrix equation using the least squares method This yields the initial storage capacity state variables and storage capacity error variables; Step S324: Calculate the inflow rate based on the initial solution results, and determine whether it meets the preset physical constraints and evaluation indicators. If it meets the requirements, proceed to step S4; otherwise, proceed to step S33.

[0028] Step S33: For matrix equations that do not meet the physical constraints and evaluation index requirements, reconstruct them into augmented matrices containing explicit constraint operators. These explicit constraint operators include boundary constraints, smoothing constraints, trend constraints, and water balance constraints. These four types of constraint operators work synergistically to improve the stability and physical rationality of the inversion results. This includes the following steps: Step S331: Reconstruct the linear matrix equation constraints into a least-squares optimization objective, and solve for the optimal solution by minimizing the squared residuals between the predicted and observed values. The formula is as follows: ; in, for The squared 2-norm of the residual vector of a matrix equation is mathematically expressed as the sum of the squares of the elements of the residual vector, i.e. ; Step S332: Explicitly construct boundary constraints, smoothing constraints, trend constraints, and water balance constraints for the solution variables, including: Boundary constraints: These control the amplitude range of state variables to avoid unreasonable extreme values, while suppressing excessive amplification of model residuals and observation errors, ensuring the physical rationality and stability of numerical calculations. The formula is as follows: ; in, This is the adjustment coefficient for the variable storage capacity. This is an adjustment coefficient for the variable error tolerance, used to balance the magnitude difference between the state variable and the error term, preventing excessive reliance on error compensation due to significant magnitude disparities from compromising physical consistency. It is adjusted by... To control the fitting accuracy between the smoothed solution and the original observed water level, the reference range is as follows: , To control the magnitude of the initial storage capacity error, the reference range is as follows: It can take integer values; Smoothing constraint: Controls the smoothness of time changes in state variables, ensuring a continuous and gradual sequence, avoiding abnormal fluctuations such as sudden increases or decreases, and maintaining good time continuity. The formula is: ; ; ; in, This is an adjustment coefficient for the reservoir capacity change rate, used to control the smoothness of the smoothed sequence. If the value is too high, it can easily lead to the loss of flood peak characteristics; a balance must be struck between smoothness and preservation of hydrological extremes. Let the first difference of the state variable, storage capacity, represent the rate of change of storage capacity. This is an adjustment coefficient for the rate of change of reservoir capacity error, used to control the magnitude of changes in reservoir capacity error, avoid local abrupt changes in the error sequence, and ensure the stability of the water level process. The first difference of the variable error represents the rate of change of the error; , The reference value range is Adjust the value according to the magnitude; Trend constraints: Used to constrain the smoothness of second-order changes in state variables, preventing unreasonable oscillations or abrupt changes in hydrological processes. The formula is: ; ; in, This is a trend adjustment coefficient, adjusted by... To ensure the water level change trend of the homogenized solution is consistent with the original data, and to avoid local fluctuations in the water level, the reference value range is: Extractable by integer. The second difference of the state variable represents the trend of the state variable's change; Water balance constraint: By constraining the balance between reservoir capacity error, reservoir capacity change, and inflow / outflow, the water balance condition is ensured during the model calculation period. To incorporate this into the optimization framework, an augmented matrix is ​​added as a penalty term during the calculation process to suppress solutions that violate water conservation. The formula is as follows: ; ; ; in, These are the weighting coefficients for water balance constraints. For length is The vector, To solve for the variable vector, The storage capacity value at the final moment of the input sequence. for Inbound volume for a given period for Outbound volume during a specific time period; Step S333: Combine the least squares terms of the fundamental matrix, the constraint terms for storage capacity, and the constraint terms for storage capacity error to obtain the overall objective function, the formula of which is: ; Step S334: Rewrite the overall objective function in matrix form to obtain the augmented matrix form, as shown in the formula: ; In the formula, the identity matrix Dimensions , Dimensions First-order differential Operator dimension is , Dimensions Second-order differential operator Dimensions ; and Specifically as follows: ; ; in, To solve for the augmented coefficient matrix of the variables, A constant vector in its augmented form; Step S335: Solve the overall objective function in augmented matrix form to obtain the unknown variables storage capacity and storage capacity error, as shown in the formula: ; in, This is the matrix regularization coefficient, with a value of 10. -6 .

[0029] Step S34: Calculate the adjustment coefficients of the physical constraint terms in the augmented matrix using trial calculations or automatically optimize hyperparameters based on a cooperative search algorithm. After adjusting the magnitude of the constraint terms, solve for the augmented matrix. Specifically, determine the adjustment coefficients of the model constraint terms based on the magnitude differences of the input sequences using trial calculations or a cooperative search algorithm. , , , and Adjust the magnitude of the constraint terms and solve for the augmented matrix.

[0030] Step S4: Output the solution variable results that meet the physical constraints and evaluation index requirements.

[0031] Figure 2 This is a comparison chart of the calculation results based on the grid search method and the comparison method. Figure 3 This image shows the calculation results of an intelligent inversion method for reservoir inflow based on multi-source error constraint fusion and a cooperative search algorithm. It can be seen that the technical solution of this invention achieves more accurate inversion of reservoir inflow, effectively eliminates negative inflow values, and its overall performance in controlling the negative value rate, water balance index, and preserving flood peak characteristics is significantly better than the comparative methods. Therefore, the technical solution of this invention effectively improves the inversion accuracy and stability of reservoir inflow under complex hydrological scenarios.

[0032] It is worth noting that all contents not described in detail in this invention are existing technologies and are well known to those skilled in the art.

[0033] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for intelligent inversion of inbound flow based on multi-source error constraint fusion, characterized in that, Includes the following steps: Step S1: Preprocess and normalize the water level and outflow monitoring data; Step S2: Construct a composite optimization function that includes a reservoir capacity time-varying error compensation term, inflow continuity regularization constraints, and a water level observation data assimilation module, including the following steps: Step S21: Obtain the original data of the reservoir's measured capacity-water level curve. Construct a nonlinear curve constraint through fitting to characterize the mapping relationship between the reservoir's water level and capacity. Based on the original inflow data, embed the constraint into the optimization function, enforce the constraint through a penalty term, and construct the inflow constraint. This constraint defines the physical boundary of the inverted flow. Combine the outflow monitoring error, implicit outflow error, and water level-capacity error into a single capacity error. Introduce the water balance formula to achieve adaptive error adjustment, and construct the water balance equation: ； in, for The reservoir capacity value corresponding to the water level at a given time. for The reservoir capacity value corresponding to the water level at a given time. for Inbound volume at any given time for Outbound volume at any given time For a moment The reservoir capacity error value; Step S22: Incorporate the temporal variation characteristics of the flow sequence into the optimization framework to construct a smoothness constraint on inflow within continuous time periods, as shown in the formula: ； in, for Inbound volume at any given time The sequence length of the inbound flow. To obtain the minimum value; Step S23: Construct and solve the optimization function expression. The optimization function expression is: ； in, and They are Observed and estimated water levels at any given time; For a moment Reservoir capacity error value, For smoothing coefficients, , For constrained weights ; Step S3: Based on the Lagrange multiplier method, a unified expression of physical constraints such as nonnegativity, continuity, and water conservation is used to derive the analytical inversion solution for the inflow and outflow. This includes the following steps: Step S31: Based on the Lagrange optimization principle, transform the optimization function into a matrix equation containing state variables and error variables. The specific dimensions and structure are as follows: ； ； ； in, , , , The coefficient submatrix, whose specific elements are determined by the boundary conditions and the equations of the interior points, For the state variable vector, For the error variable vector, To observe the reservoir capacity corresponding to the water level, , , They are respectively the dimensions of , , Known variables , The coefficient matrix, for The 0 matrix, To solve for the coefficient matrix of the variables, To solve for the variable vector, It is a constant vector; Step S32: Optimize the constraint weights and smoothing coefficients using grid search or cooperative search algorithms. Specifically, use grid search to systematically traverse the smoothing coefficients, and use cooperative search to perform global optimization of the combination of constraint weights and smoothing coefficients and solve the matrix. Reconstruct the linear matrix equation constraints into a least-squares optimization objective, solve for the optimal solution by minimizing the squared residual between the predicted and observed values, and determine whether the result meets the physical constraints and evaluation index requirements. Step S33: For matrix equations that do not meet the physical constraints and evaluation index requirements, reconstruct them into augmented matrices containing explicit constraint operators, where explicit constraint operators include boundary constraints, smoothing constraints, trend constraints and water balance constraints. Step S34: Perform trial calculations on the adjustment coefficients of the physical constraint terms in the augmented matrix or automatically optimize the hyperparameters based on the cooperative search algorithm, and solve the augmented matrix after adjusting the magnitude of the constraint terms; Step S4: Output the solution variable results that meet the physical constraints and evaluation index requirements.

2. The intelligent inversion method for inbound flow based on multi-source error constraint fusion according to claim 1, characterized in that: Step S1 includes the following steps: Step S11: Align the raw monitoring data with the time dimension to ensure that key data are consistent at the time nodes. Key data includes, but is not limited to, water level and outflow. Step S12: For individual missing values, use linear interpolation to complete them; Step S13: Based on the reservoir water level-capacity relationship curve, convert the discrete water level time series into the corresponding reservoir capacity time series to generate the dynamic change data of reservoir capacity required for model operation. The normalization formula is as follows: ； in, For numerical sequences that require normalization calculations, For data sequences that need to be standardized, For sequence The midpoint value of the sequence after sorting from largest to smallest This is the standardized data.

3. The intelligent inversion method for inbound flow based on multi-source error constraint fusion according to claim 1, characterized in that: Step S21 includes the following steps: Step S211: Construct nonlinear curve constraints to characterize the mapping relationship between reservoir water level and reservoir capacity, ensuring the physical correspondence between reservoir capacity estimation and water level observation. The formula is: ； in, This is the water level-capacity curve of the reservoir. for The water level at that moment; Step S212: Construct inbound quantity constraints to constrain the physically reasonable boundaries of the inverted flow, avoiding physically unreasonable negative flow values. The formula is: ； in, for The original inbound flow at any given moment for Time's up The time interval between moments; Step S213: Construct outbound quantity constraints to strictly control the outbound flow rate to be greater than or equal to 0. The formula is: ； in, for The original outbound flow at any given moment.

4. The intelligent inversion method for inbound flow based on multi-source error constraint fusion according to claim 1, characterized in that: In step S23, the flow smoothing term in the optimization function characterizes the natural runoff process that is not significantly regulated by human activities by constraining the slow variation of inflow over a short period of time. When human activities have a strong effect on runoff regulation in the study area, the applicability of the simplification assumption decreases, and the optimization strategy is adjusted in combination with the actual hydrological situation.

5. The intelligent inversion method for inbound flow based on multi-source error constraint fusion according to claim 1, characterized in that: Step S31 includes the following steps: Step S311: Substitute the nonlinear curve constraints, inflow constraints, outflow constraints, and water balance constraints into the optimization function, transforming the optimization function into a function expression containing known and unknown variables. The formula is as follows: ； in, for The reservoir capacity value corresponding to the water level at a given moment; Step S312: Based on the Lagrange optimization principle, take partial derivatives with respect to the unknown variables to obtain two partial differential equations. Set the partial differential equations to zero, rearrange them to form a system of equality constraint equations, and calculate... , Internal points Boundary points and expanding boundary points Equality constraints at that time; Step S313: Further rearrange the system of equality constraint equations into matrix form.

6. The intelligent inversion method for inbound flow based on multi-source error constraint fusion according to claim 1, characterized in that: In step S31: ； ； ； ； ； The state variable vector and error variable vector can be solved by matrix inversion, using the following formula: ； in, This is the matrix transpose.

7. The intelligent inversion method for inbound flow based on multi-source error constraint fusion according to claim 1, characterized in that: Step S32 includes the following steps: Step S321: Use a grid search algorithm to smooth the low-dimensional parameter coefficients. Perform a systematic traversal, the traversal range is Initial screening identified smoothing coefficients that balance flow smoothness with observation fit. Candidate values; Step S322: Use a cooperative search algorithm to adjust the constraint weights. With smoothing coefficient Global optimization is performed using high-dimensional coefficient combinations, with the optimization range being... , The optimization objective is to minimize the value of the composite optimization function while simultaneously satisfying the inflow rate. Preliminary physical constraints; Step S323: Solve the matrix equation using the least squares method This yields the initial storage capacity state variables and storage capacity error variables; Step S324: Calculate the inflow rate based on the initial solution results, and determine whether it meets the preset physical constraints and evaluation indicators. If it meets the requirements, proceed to step S4; otherwise, proceed to step S33.

8. The intelligent inversion method for inbound flow based on multi-source error constraint fusion according to claim 1, characterized in that: In step S33, the standard form is transformed into an augmented matrix form containing explicit constraint operators. This involves explicitly constructing boundary constraints, smoothing constraints, trend constraints, and water balance constraints for the solution variables (sumption capacity, error), including the following steps: Step S331: Reconstruct the linear matrix equation constraints into a least-squares optimization objective, and solve for the optimal solution by minimizing the squared residuals between the predicted and observed values. The formula is as follows: ； in, for The squared 2-norm of the residual vector of a matrix equation is mathematically expressed as the sum of the squares of the elements of the residual vector, i.e. ; Step S332: Explicitly construct boundary constraints, smoothing constraints, trend constraints, and water balance constraints for the solution variables, including: Boundary constraints: control the amplitude range of state variables and suppress excessive amplification of model residuals and observation errors. The formula is: ； in, This is the adjustment coefficient for variable storage capacity; the reference range is... , This is the adjustment coefficient for the variable error tolerance; the reference range is... ; Smoothing constraint: controls the smoothness of time-varying state variables, the formula is: ； ； ； in, This is the adjustment coefficient for the rate of change in storage capacity. Let the first difference of the state variable, storage capacity, represent the rate of change of storage capacity. This is the adjustment coefficient for the rate of change of storage capacity error. Let be the first difference of the variable error, representing the rate of change of the error. , The reference value range is Adjust the value according to the magnitude; Trend constraint: Constrains the smoothness of second-order changes in state variables, with the following formula: ； ； in, This is a trend adjustment coefficient, with a reference range of values. , The second difference of the state variable represents the trend of the state variable's change; Water balance constraint: By constraining the balance between reservoir capacity error, reservoir capacity change, and inflow / outflow, an augmented matrix is ​​added as a penalty term during the calculation to suppress solutions that violate water conservation. The formula is as follows: ； ； ； in, These are the weighting coefficients for water balance constraints. For length is The vector, To solve for the variable vector, The storage capacity value at the final moment of the input sequence. for Real-time inbound volume for Real-time outbound volume; Step S333: Combine the least squares terms of the fundamental matrix, the constraint terms for storage capacity, and the constraint terms for storage capacity error to obtain the overall objective function, the formula of which is: ； Step S334: Rewrite the overall objective function in matrix form to obtain the augmented matrix form, as shown in the formula: ； ； ； in, To solve for the augmented coefficient matrix of the variables, A constant vector in its augmented form; Step S335: Solve the overall objective function in augmented matrix form to obtain the unknown variables storage capacity and storage capacity error, as shown in the formula: ； in, is the matrix regularization coefficient.

9. The intelligent inversion method for inbound flow based on multi-source error constraint fusion according to claim 1, characterized in that: Step S34 specifically involves: determining the adjustment coefficients of the model constraint terms based on the magnitude differences of the input sequences, using either a trial-and-error algorithm or a cooperative search algorithm. , , , and Adjust the magnitude of the constraint terms and solve for the augmented matrix.

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